One of a cover letter's principle functions is to introduce you to a prospective employer. In the case of an internal opening, that job is done, though the company knows you in the operational role you currently occupy. Use a conventional, three-section cover letter layout to freshly reintroduce yourself as the ideal candidate for the management vacancy, expanding on your resume qualifications.
Paragraph One: The Appetizer
Take charge of the introduction, and don't state the obvious. The company knows who you are, and if you know who will read your letter, address them personally. Recruiters want enthusiasm from managers so start it here. Be excited to apply for the manager's job opening, and tell them so, quickly and concisely. If you know you can achieve a specific result, say so. Two or three sentences is plenty for the first paragraph.
Paragraph Two: The Entree
Don't rewrite your resume. The cover letter is your tool to create buzz, so don't put all the highlights on top or your buzz will die when the reader turns the page. Outside applicants go to lengths to learn about your company for paragraph two. You already know it, so show it. Put your personality and passion on display. If you led a safety team, say so. Your biggest challenge may be being seen as a leader, so point to those skills or add something expansive and enhancing.
Paragraph Three: Dessert
Ask for the interview. Close the sale. Managers get results, so show your attitude is goal-oriented. Remember that the cover letter is marketing. The meat-and-potatoes about you is in your resume and your personnel file. Your drive and enthusiasm are not, so use the cover letter to expand on these. Don't overreach. Your cover letter and resume secure the interview, then the interview secures the job.
Double Check the Menu
Check and double-check your cover letter for accuracy. Have a colleague and friend proofread for you. Applications are discarded for mistakes, even tiny ones, and even by people who spell poorly in their own correspondence. You will not get special consideration for this because you work there. There are no excuses for mistakes.